IIT JEE , AIEEE Forum - Physics , Mechanics

winner10789

Two masses m and M r attached to a vertical axis by weightless threads of combined lenghts L.they are set in rotational motion about this axis with constant angular velocity

.If the tensions in the threads are the same during motion , the distance of M from the axis is :

a)ML/M+m

b)mL/M+m

c)M+m/M*L

d)M+m/m*L

rooney

Let distance of mass m from axis be l
and that of mass M from axis be (L-l)
Let velocities of m and M be v and V repectively

w= v/l = V / (L - l) - [1]

T₁ = mv²/l
T₂=MV²/(L-l)

T₁=T₂

So, mv²/l = MV²/(L-l) -[2]

Using [1] in [2] and solving
ml=ML - Ml
So, l = ML / (m + M)

Distance of M from axis = L - l = mL / (m+M) which is option [2]

iitkgp_bipin

Well done Rooney.

Constant angular velocity = v/l = V/(L-l)...........(1)

Tension = mv²/l = MV²/(L-l)............(2)

Using these two : l = ML/(M+m)

So distance of M from axis = L-l = mL/(M+m)

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